Tính liên thông của tập nghiệm hữu hiệu yếu cho bài toán tối ưu tập không lồi
Abstract
This paper considers a nonconvex set optimization problem and discusses connectedness conditions for its weakly efficient solution set. Firstly, various concepts of connectedness for a set-valued map are proposed. Secondly, sufficient conditions for the connectedness of an extension of the oriented distance of Hiriart-Urruty are formulated. Finally, the connectedness properties of a weakly efficient solution set to such problem are investigated via the extension of the oriented distance of Hiriart-Urruty.
Tóm tắt
Bài báo này xem xét một bài toán tối ưu tập không lồi và thảo luận các điều kiện liên thông cho tập nghiệm hữu hiệu yếu của nó. Đầu tiên, các khái niệm khác nhau về tính liên thông cho ánh xạ có giá trị tập được đề xuất. Thứ hai, các điều kiện đủ cho tính liên thông cho một dạng mở rộng của hàm khoảng cách định hướng của Hiriart-Urruty được trình bày. Cuối cùng, tính liên thông của tập nghiệm hữu hiệu yếu cho bài toán trên được nghiên cứu thông qua dạng mở rộng của hàm khoảng cách định hướng của Hiriart-Urruty.
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